\chapter{Sub-seasonal Forecasts}\label{chap:forecasts}
The final step of the pipeline consists in transposing the quantification step into a medium-term outlook. This is achieved by injecting the knowledge derived from the product presented in Section \ref{sec:s2s}, thereby calibrating it by means of our predicted distributions. As previously mentioned, one limitation of such forecasts are in the clustering assumption they rely on. Indeed, ECMWF \parencite{p17442} adopts a 5-clusters ensemble model, not encompassing the entirety of the variability of weather regimes, and thus needing the presence of an unknown cluster to take into account noisier assignments. Since our application strictly requires a 4-clusters scenario, we approximate the fifth missing distribution by assigning probability mass to the other distributions, proportionally to the assigned weight each regime has. Of course, whether the ``Unknown'' cluster is predicted with a 100\% probability, we keep it uninformative assigning uniform probabilities to all the clusters' distributions.\\
The calibration step is thus obtained by computing a weighted sum of the four distributions. Although for some energy variables the distributions referred to the regimes are really close, we observe that minimum shifts in the mean and standard deviation often translate into typically different outlooks for the predicted window of 45 days.\\
In our analysis, we are also able to take into account known biases of these forecasts. Figure \ref{fig:avg_weights_ECMWF} reports the tendency of these statistical models to favour Zonal flow in the long-term, while striving with the NAO- signals. Indeed, as a general pattern, the average probabilities assigned to the regimes should gradually converge to an uninformative fashion, as the forecasted step is farther in time. However, the NAO+ regime's presence (conceptually equivalent to Zonal flow) increases in importance. Unfortunately, given the novelty of the product, the chart is only referred to the last winter predictions, thus being biased on the events which charactrized it. We clearly see in the initial steps the overall high probabilities assigned to NAO-, reflecting correctly the tendency of the regimes during that season. The peak in Scandinavian Blocking is instead difficult to be justified, given that its occurrence in Winter 2020 resulted to be below normal.

\begin{figure}[!htbp]
    \centering
    \includegraphics[width = .75\textwidth]{imgs/avg_weights_ecmwf.png}
    \caption{Average weights of the sub-seasonal forecasts of ECMWF by regime}
    \label{fig:avg_weights_ECMWF}
\end{figure}
We adopt this analysis as a prior belief, mainly to establish some high-level criteria to identify whether some signals could be considered enough strong, and thus potentially accurate with some weeks of anticipation.
\input{content/chapters/sections/5_1usecases}


%Model biased to show Zonal (NAO+) flow in the long period
%Chart high NAO-/SB at the beginning, biased by only data of last winter